Blender Armature Weight Painting - Bone does not move how he should
Select your mesh and go into edit mode. Select single vertices and check Vertex Weights right in the properties shelf (see screenshot below). This way you can check for each vertex if it is influenced by an unwanted bone.

Another frequent error while rigging is if your mesh is mirrored. For modelling this is great, but when animating it's better to apply the modifier first.